Real-Time Optimal Parametric Design of a Simple Infiltration-Evaporation Model Using the Assess-Predict-Optimize (APO) Strategy

Abstract

Optimal parametric design of a system must be able to respond quickly to short term needs as well as long term conditions. To this end, we present an Assess-Predict-Optimize (APO) strategy which allows for easy modification of a system’s characteristics and constraints, enabling quick design adaptation. There are three components to the APO strategy: Assess - extract necessary information from given data; Predict - predict future behavior of system; and Optimize – obtain optimal system configuration based on information from the other components. The APO strategy utilizes three key mathematical ingredients to yield real-time results which would certainly conform to given constraints: dimension reduction of the model, a posteriori error estimation, and optimization methods. The resulting formulation resembles a bilevel optimization problem with an inherent nonconvexity in the inner level. Using a simple infiltration-evaporation model to simulate an irrigation system, we demonstrate the APO strategy’s ability to yield real-time optimal results. The linearized model, described by a coercive elliptic partial differential equation, is discretized by the reduced-basis output bounds method. A primal-dual interior point method is then chosen to solve the resulting APO problem.